Dutch voters are going to the polls in the first of three key European votes this year in which populist parties, heartened by Britain’s Brexit vote and Donald Trump’s US victory, are seeking electoral breakthroughs.

With voting under way in bright sunshine on Wednesday, a leading polling aggregator showed a clear lead for the liberal VVD party of the prime minister, Mark Rutte, who was predicted to win between 24 and 28 seats in the 150-seat parliament.

The far-right Freedom party (PVV), led by the anti-Islam populist Geert Wilders, was forecast to win 19-23 seats, barely ahead of the Christian Democrats (CDA) on 19-21 seats and the progressive liberals of Democrats 66 (D66) with 17-19, both natural coalition partners for Rutte.

The election will not, however, produce a clear winner, with as many as 15 parties set to return at least one MP and none likely to gain more than 17% of seats: months of complex coalition negotiations lie ahead.

Wilders cast his ballot at a polling station in The Hague early on Wednesday, telling reporters afterwards: “Whatever the outcome of the election today, the genie will not go back into the bottle. People feel misrepresented.”

But Rutte said he hoped the election, which has been overshadowed since the weekend by an increasingly acrimonious diplomatic standoff between Turkey and a number of EU capitals, would slow the populists’ momentum.

What are the issues in the Dutch election?

The fundamentals of the economy are recovering well from the global financial crisis, with unemployment at a five-year low and economic growth at 2.3%. Healthcare and pensions are significant topics of debate, but in the absence of major economic concerns the biggest issue is immigration and integration. The agenda has been driven by the anti-Islam and anti-EU populist rhetoric of Geert Wilders, as well as the wider political climate across Europe. Dominant themes of discussion have included multiculturalism, globalisation, sovereignty, Dutch values, and how far the EU works – or doesn’t work – for the Netherlands. Read our comprehensive preview

The vote was “a chance for a big democracy like the Netherlands to make a point, to stop this domino effect ... of the wrong sort of populism,” Rutte said, though he warned there was still a chance the PVV might be the biggest party.

Up to 30% of voters were undecided going into polling day, leaving the outcome unpredictable. But Wilders, who has pledged to “de-Islamise” the Netherlands and take it out of the EU, is unlikely to enter government however well he fares: no other main party will work with the PVV in coalition.

Nonetheless, after the UK’s vote to leave the EU and Trump’s “America first” upset last year, a first-place finish for the PVV would rock Europe – with the far-right Front National leader, Marine Le Pen, set to make the run-off in France’s presidential poll in May and the Eurosceptic Alternative für Deutschland (AfD) on target to win its first federal seats in Germany later in the year.

Analysts said Rutte had benefited from his handling of the fierce row with Turkey over the government’s refusal to allow Turkish ministers to address rallies of Dutch Turks before a referendum next month on plans to grant Turkey’s president, Recep Tayyip Erdoğan, sweeping new powers.

In a campaign dominated by Wilders’ core themes of immigration and integration, the row has “allowed Rutte to show himself as a statesman – and to send a Turkish minister packing”, said André Krouwel, a political scientist at Amsterdam’s Free University.

“What better publicity could a politician want a few days before an election?” Klouwer said. “Rutte was able to show he could actually expel Turks, and to tell Wilders: ‘You’re just sitting there, tweeting’ … This has won Rutte the election.”

In a possibly unrelated incident, two big Dutch voting information websites were targeted by a cyberattack on Wednesday. Several Twitter accounts including those of the European parliament, the German newspaper Die Welt and Amnesty International were also hacked, apparently by pro-Erdoğan activists.

As many as 13 million Dutch voters are expected to cast their ballots in the poll, with polling stations closing at 9pm. Provisional results are expected to be known by midnight, with the final count formally announced on 21 March.

Voting in The Hague, Sonja van Spronsen, a 45-year-old office worker, said she hoped the next government could produce a “good, convivial Netherlands. Not just arguing and complaining but with a good positive vision of how to move forward that we can all get behind.”

Van Spronsen, who voted for “one of the parties on the right”, did not rule out a role for the PVV. “It’s a sense of powerlessness,” she said. “The average person is dissatisfied to an extent – a lot of Dutch think the same, but just don’t say it in such strong terms.”

Followed by a scrum of reporters, Jesse Klaver, the 30-year-old leader of the Green Left party, which is set to quadruple its MPs to between 16 and 18, voted mid-morning and directed his message at younger voters: “Above all, get out and vote, and vote for Green-Left because it’s the party of the future.”

Ben Baks, a 60-year-old civil servant, said he voted Green-Left but wanted to see a rainbow coalition combining parties from left and right. “Whatever happens, we need a country that’s governable,” he said. “We need to send out a strong signal to other European countries.”

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But Donny Bonsink, a 24-year-old chef, predicted a strong showing for Wilders. “Islamisation in the Netherlands has to stop,” he said. “We’ve had governments trying to make immigration work for 40 years and all it’s brought us is problems. People are angry.”

Informal coalition talks between at least four and probably five parties will begin on Thursday, although the process does not formally get under way until 23 March, when the new parliament sits for the first time.

If the VVD finishes as the largest party, Rutte will seek a majority of 76 seats, most likely with other mainstream parties including the CDA, the centre-left Labour party (PvdA) and D66. Klaver’s Green-Left could well play a kingmaker role, though it would face major policy conflicts with the centre-right.

Coalition building, especially when so many parties are involved, could take months: the average in the Netherlands is three months, but in 1977 the process took more than 200 days.